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Asda said the phasing out of the 5p bag is just one phase of the supermarket's war on plastic, with cheap re-usable coffee cups coming in and plastic cutlery and cups disappearing from cafes and offices.

Asda chief executive Roger Burnley said: “Where we are able to go faster and harder to remove avoidable plastics from our products, we will.

“Our logic is to remove plastic wherever we can, and where it is required, to make it as recyclable as possible.”

Tesco said that in the last year alone, the number of 5p bags it has sold has fallen by 72 per cent in stores.

Since the law change for English stores in October 2015, Tesco has handed out 1.5 billion fewer bags than it would normally have done over the same period.

Online shoppers also have the choice of the 5p bags or no bags at all and 57 per cent now choose bagless deliveries but the initial trial is simply in stores in Norwich, Aberdeen and Dundee.

A spokeswoman for Tesco told trade journal The Grocer that the trial was intended 'to look at the impact on bag usage if we remove single-use carrier bags.